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19-year-old Fleetwood fired a six-under-par 65 at North Berwick to win by two holes.
"The first few holes were a bit of a struggle," said the 2008 Amateur Championship runner-up.
"Towards the end though, when I really needed it, I played well. As long as I play well, I think I've got a good chance of going all the way."
Stiggy Hodgson, was assertive in his display, beating Royal Liverpool's Tom Boys by four holes.
Hodgson said: "You can't get over-confident, but I feel confident enough.
"I'm striking it great and putting well, which is nice. I can't get too excited yet, though - it's only the first round."
24-year-old Paisley saw off Italy's Mattia Miloro with a three-hole victory.
The University of Tennessee graduate said: "The Walker Cup gave me lots of confidence - I had two halves in the singles there, and both were really good games. It gave me confidence that I can play on a big stage." Others to make it through were Welshman Rhys Enoch, Scotland's James Byrne, Bolivia's Sebastian MacLean, Yuki Usami of Japan and Sweden's Henrik Norlander.
The draw is available to view on RandA.org (opens in new tab), with the winner of the 36-hole final on June 19 gaining Open Championship and Masters exemptions. For more information call the R&A on 01334 460000.
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